theorem Th27:
  M is strong_limit implies M is limit_cardinal
proof
  assume
A1: M is strong_limit;
  assume not M is limit_cardinal;
  then consider N such that
A2: M = nextcard N;
  M c= exp(2,N) by A2,Th24;
  then
A3: not exp(2,N) in M by CARD_1:4;
  N in M by A2,CARD_1:18;
  hence contradiction by A1,A3;
end;
